FTM breastfeeding question

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If breast milk doesn't typically come in until 2-3 days after giving birth, do you still try to breastfeed in the hospital when baby is born? Isn't it kind of mean to let the baby suck if it's not really going to get anything? I'd also imagine that this is what causes nipple soreness from the getgo, sucking on a dry well basically. 
Is this why hospitals typically may want to give the infant formula to supplement breastfeeding so they don't lose so much weight initially?